CFun ( Frame4J -- the Java framework de.frame4j... )

All Known Implementing Classes:

Complex
```
public interface CFun
```
Special functions collection (the subset used by Complex).

This class features some mathematical functions not to be found in java.lang.Math. Most of them are used by Complex.

If at least one argument is NaN (invalid, not a number) the returned result will be NaN if not explicitly stated otherwise.

© Copyright 1999 - 2003, 2005 Albrecht Weinert

Version:

44 (6.05.2021)

Author:

Albrecht Weinert

See Also:

de.frame4j.math, Complex

Nested Class Summary

Nested Classes
Modifier and Type Interface and Description

static class CFun.Impl

Nested Classes
Modifier and Type	Interface and Description
`static class`	`CFun.Impl`

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`D_NaN` The invalid value (NaN) for double.
`static long`	`D_SIGN_MASK` Mask for the sign bit in IEEE 754 double coding.
`static long`	`D_VALUE_MASK` Mask for exponent and mantissa in IEEE 754 double coding.
`static double`	`EPSILON_SMALL` The smallest relative spacing for doubles.
`static MathContext`	`FOUR_MC` A mathematical context with precision 4.
`static int`	`NOSH` Number of special hash values.
`static double`	`PI` pi .
`static double`	`PI_2` pi/2 .
`static double`	`PI_3_4` 3pi/4 .
`static double`	`PI_4` pi/4 .

Method Summary

All Methods Static Methods Default Methods
Modifier and Type	Method and Description
`static StringBuilder`	`append(StringBuilder bastel, double dD, int prec, String[] forms)` Append the text representation of a double.
`static double`	`asinh(double x)` Arcussinus hyperbolicus / inverse (arc) hyperbolic sine.
`static double`	`cosh(double x)` Hyperbolic cosine.
`static double`	`csevl(double x, double[] coef)` Evaluate a Chebyshev series.
`static MathContext`	`getMathContext(int prec)` Return a mathematical context.
`static int`	`hashCode(double x, double y)` A hash value for a double pair.
`static boolean`	`sign(double val)` The sign of a double.
`static double`	`sign(double val, double sign)` Value of x with the sign of y.
`static double`	`sinh(double x)` Hyperbolic sine.
`static double`	`tanh(double x)` Tangens hyperbolicus / hyperbolic tangent .

Field Detail
- EPSILON_SMALL
```
static final double EPSILON_SMALL
```
  The smallest relative spacing for doubles.
  
  See Also:
  
  Constant Field Values
- D_NaN
```
static final double D_NaN
```
  The invalid value (NaN) for double.
  
  D_NaN ist Double.NaN.
  
  See Also:
  
  Constant Field Values
- PI
```
static final double PI
```
  pi .
  
  See Also:
  
  Constant Field Values
- PI_2
```
static final double PI_2
```
  pi/2 .
  
  See Also:
  
  Constant Field Values
- PI_4
```
static final double PI_4
```
  pi/4 .
  
  See Also:
  
  Constant Field Values
- PI_3_4
```
static final double PI_3_4
```
  3pi/4 .
  
  See Also:
  
  Constant Field Values
- D_SIGN_MASK
```
static final long D_SIGN_MASK
```
  Mask for the sign bit in IEEE 754 double coding.
  
  This is also the -0.0 (negative null) in EEE 754.
  
  See Also:
  
  Constant Field Values
- D_VALUE_MASK
```
static final long D_VALUE_MASK
```
  Mask for exponent and mantissa in IEEE 754 double coding.
  
  See Also:
  
  Constant Field Values
- NOSH
```
static final int NOSH
```
  Number of special hash values.
  
  See Also:
  
  hashCode(), Constant Field Values
- FOUR_MC
```
static final MathContext FOUR_MC
```
  A mathematical context with precision 4.

Method Detail

sign
```
static boolean sign(double val)
```
The sign of a double.

true is returned, if the sign bit according to IEEE 754 coding is set. This will be done for all types of values including the zeros, infinity and of all the (too many) NaN codings.

See Also:

sign(double, double)

sign
```
static double sign(double val,
                   double sign)
```
Value of x with the sign of y.

This method returns the value of the parameter val with the parameter's sign sign. This will also be done if parameter sign is NaN.

If sign is NaN in Java's canonical encoding (0x7ff8000000000000L) that will be positive.

Parameters:

val - take the value

sign - take the sign (only if val is not NaN)

See Also:

sign(double)

hashCode

static int hashCode(double x,
                    double y)

A hash value for a double pair.

This method calculates a significant hash value for a pair of double numbers according to the requirements of the class Complex (complex numbers). But it is nevertheless suitable for other number pairs like common co-ordinates or factors in a transformation.

For the hash values returned the following holds:

x	y	Hash-Wert	arcus	Grad
NaN	beliebig	0	D_NaN	-
any	NaN	0	D_NaN	-
+infinit	finite	1	0.0	0
+infinit	+infinit	2	PI_4	45
finite	+infinit	3	PI_2	90
-infinit	+infinit	4	PI_3_4	135
-infinit	finite	5	PI	180
-infinit	-infinit	6	-PI_3_4	225
finite	-infinit	7	-PI_2	270
+infinit	-infinit	8	-PI_4	315
0.0	0.0	9	0.0	0
1.0	0.0	10	0.0	0
0.0	1.0	11	PI_2	90
-1.0	0.0	12	PI	180
0.0	-1.0	13	-PI_2	270

beside that the following holds for the hash values returned:

No other pairs of x and y will return the values 0 to 13.
No values < 0 are returned.

Hint: The values in the radian measure (arcus) column are named constants (finals) in this class.

Parameters:: x - first pair value; y - second pair value
Returns:: a hash value >= 0
See Also:: NOSH, D_NaN, PI, PI_2

csevl
```
static double csevl(double x,
                    double[] coef)
```
Evaluate a Chebyshev series.

This (package) helper method takes for granted that the array of coefficients coefis not null and does contain no NaN as well as that the argument x is in the allowed range (mostly 0..1).

Under all other conditions the result is not predictable and exceptions might be thrown unexpectedly.

Parameters:

x - the argument

coef - the field (vector) of coefficients

sinh
```
static double sinh(double x)
```
Hyperbolic sine.

cosh
```
static double cosh(double x)
```
Hyperbolic cosine.

tanh
```
static double tanh(double x)
```
Tangens hyperbolicus / hyperbolic tangent .

asinh
```
static double asinh(double x)
```
Arcussinus hyperbolicus / inverse (arc) hyperbolic sine.

append
```
static StringBuilder append(StringBuilder bastel,
                            double dD,
                            int prec,
                            String[] forms)
```
Append the text representation of a double.

The array forms, if null, will default to {"", "-", "0.00", "NaN", "inf."}. As might be obvious forms has to contain the prefixes for positive and negative, and the presentments of zero, infinity and invalid.

Parameters:

bastel - the StringBuilder to append to (if null one is made)

dD - the value to be formatted

prec - the decimal precision (2..18; default 4)

forms - an array of length 5 containing no null String, or null

Returns:

bastel

getMathContext
```
static MathContext getMathContext(int prec)
```
Return a mathematical context.

This method returns a (cached) MathContext for precisions in the range of 0 to 18.

Parameters:

prec - a precision 0..18 (default 4, 0 meaning unlimited precision)

Returns:

a mathematical context

See Also:

FOUR_MC, MathContext.UNLIMITED

Interface CFun

Nested Class Summary

Field Summary

Method Summary

Field Detail

EPSILON_SMALL

D_NaN

PI

PI_2

PI_4

PI_3_4

D_SIGN_MASK

D_VALUE_MASK

NOSH

FOUR_MC

Method Detail

sign

sign

hashCode

csevl

sinh

cosh

tanh

asinh

append

getMathContext